ScottTestRobot at 21:58, 1 September 2005

2005-09-01T21:58:01Z

DrorsRobot at 22:41, 31 August 2005

2005-08-31T22:41:38Z

← Older revision		Revision as of 18:41, 31 August 2005
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	coloured_jones_3 = <math>q^{36}-5 q^{35}+3 q^{34}+14 q^{33}-42 q^{31}-29 q^{30}+97 q^{29}+92 q^{28}-125 q^{27}-241 q^{26}+121 q^{25}+429 q^{24}-9 q^{23}-638 q^{22}-208 q^{21}+788 q^{20}+534 q^{19}-856 q^{18}-897 q^{17}+799 q^{16}+1254 q^{15}-631 q^{14}-1578 q^{13}+413 q^{12}+1801 q^{11}-125 q^{10}-1978 q^9-139 q^8+2034 q^7+443 q^6-2048 q^5-682 q^4+1920 q^3+929 q^2-1730 q-1066+1404 q^{-1} +1145 q^{-2} -1050 q^{-3} -1080 q^{-4} +677 q^{-5} +910 q^{-6} -360 q^{-7} -683 q^{-8} +152 q^{-9} +438 q^{-10} -39 q^{-11} -243 q^{-12} +6 q^{-13} +111 q^{-14} + q^{-15} -50 q^{-16} +10 q^{-17} +15 q^{-18} -7 q^{-19} -5 q^{-20} +3 q^{-21} +4 q^{-22} -4 q^{-23} + q^{-24} </math> \|		coloured_jones_3 = <math>q^{36}-5 q^{35}+3 q^{34}+14 q^{33}-42 q^{31}-29 q^{30}+97 q^{29}+92 q^{28}-125 q^{27}-241 q^{26}+121 q^{25}+429 q^{24}-9 q^{23}-638 q^{22}-208 q^{21}+788 q^{20}+534 q^{19}-856 q^{18}-897 q^{17}+799 q^{16}+1254 q^{15}-631 q^{14}-1578 q^{13}+413 q^{12}+1801 q^{11}-125 q^{10}-1978 q^9-139 q^8+2034 q^7+443 q^6-2048 q^5-682 q^4+1920 q^3+929 q^2-1730 q-1066+1404 q^{-1} +1145 q^{-2} -1050 q^{-3} -1080 q^{-4} +677 q^{-5} +910 q^{-6} -360 q^{-7} -683 q^{-8} +152 q^{-9} +438 q^{-10} -39 q^{-11} -243 q^{-12} +6 q^{-13} +111 q^{-14} + q^{-15} -50 q^{-16} +10 q^{-17} +15 q^{-18} -7 q^{-19} -5 q^{-20} +3 q^{-21} +4 q^{-22} -4 q^{-23} + q^{-24} </math> \|
	coloured_jones_4 = <math>q^{60}-5 q^{59}+3 q^{58}+14 q^{57}-6 q^{56}-9 q^{55}-56 q^{54}+8 q^{53}+126 q^{52}+73 q^{51}+14 q^{50}-370 q^{49}-285 q^{48}+281 q^{47}+586 q^{46}+741 q^{45}-701 q^{44}-1468 q^{43}-673 q^{42}+880 q^{41}+2997 q^{40}+747 q^{39}-2369 q^{38}-3644 q^{37}-1547 q^{36}+4943 q^{35}+4858 q^{34}+171 q^{33}-6159 q^{32}-7414 q^{31}+2969 q^{30}+8585 q^{29}+6684 q^{28}-4473 q^{27}-13248 q^{26}-3251 q^{25}+8247 q^{24}+13620 q^{23}+1429 q^{22}-15524 q^{21}-10334 q^{20}+4000 q^{19}+17807 q^{18}+8401 q^{17}-14277 q^{16}-15584 q^{15}-1524 q^{14}+19134 q^{13}+14190 q^{12}-11277 q^{11}-18735 q^{10}-6782 q^9+18435 q^8+18492 q^7-7057 q^6-19850 q^5-11705 q^4+15253 q^3+20794 q^2-1299 q-17650-15351 q^{-1} +8955 q^{-2} +19206 q^{-3} +4533 q^{-4} -11417 q^{-5} -15187 q^{-6} +1703 q^{-7} +13052 q^{-8} +7028 q^{-9} -3926 q^{-10} -10460 q^{-11} -2413 q^{-12} +5657 q^{-13} +5148 q^{-14} +477 q^{-15} -4606 q^{-16} -2335 q^{-17} +1225 q^{-18} +1994 q^{-19} +1092 q^{-20} -1214 q^{-21} -882 q^{-22} +41 q^{-23} +342 q^{-24} +451 q^{-25} -215 q^{-26} -141 q^{-27} -5 q^{-28} -13 q^{-29} +97 q^{-30} -43 q^{-31} -2 q^{-32} +12 q^{-33} -17 q^{-34} +13 q^{-35} -9 q^{-36} +3 q^{-37} +4 q^{-38} -4 q^{-39} + q^{-40} </math> \|		coloured_jones_4 = <math>q^{60}-5 q^{59}+3 q^{58}+14 q^{57}-6 q^{56}-9 q^{55}-56 q^{54}+8 q^{53}+126 q^{52}+73 q^{51}+14 q^{50}-370 q^{49}-285 q^{48}+281 q^{47}+586 q^{46}+741 q^{45}-701 q^{44}-1468 q^{43}-673 q^{42}+880 q^{41}+2997 q^{40}+747 q^{39}-2369 q^{38}-3644 q^{37}-1547 q^{36}+4943 q^{35}+4858 q^{34}+171 q^{33}-6159 q^{32}-7414 q^{31}+2969 q^{30}+8585 q^{29}+6684 q^{28}-4473 q^{27}-13248 q^{26}-3251 q^{25}+8247 q^{24}+13620 q^{23}+1429 q^{22}-15524 q^{21}-10334 q^{20}+4000 q^{19}+17807 q^{18}+8401 q^{17}-14277 q^{16}-15584 q^{15}-1524 q^{14}+19134 q^{13}+14190 q^{12}-11277 q^{11}-18735 q^{10}-6782 q^9+18435 q^8+18492 q^7-7057 q^6-19850 q^5-11705 q^4+15253 q^3+20794 q^2-1299 q-17650-15351 q^{-1} +8955 q^{-2} +19206 q^{-3} +4533 q^{-4} -11417 q^{-5} -15187 q^{-6} +1703 q^{-7} +13052 q^{-8} +7028 q^{-9} -3926 q^{-10} -10460 q^{-11} -2413 q^{-12} +5657 q^{-13} +5148 q^{-14} +477 q^{-15} -4606 q^{-16} -2335 q^{-17} +1225 q^{-18} +1994 q^{-19} +1092 q^{-20} -1214 q^{-21} -882 q^{-22} +41 q^{-23} +342 q^{-24} +451 q^{-25} -215 q^{-26} -141 q^{-27} -5 q^{-28} -13 q^{-29} +97 q^{-30} -43 q^{-31} -2 q^{-32} +12 q^{-33} -17 q^{-34} +13 q^{-35} -9 q^{-36} +3 q^{-37} +4 q^{-38} -4 q^{-39} + q^{-40} </math> \|
	coloured_jones_5 = \|		coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_6 = \|		coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_7 = \|		coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> \|
	computer_talk =		computer_talk =
	<table>		<table>
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	<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>		<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
	</tr>		</tr>
	<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 122]]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 122]]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 6, 2, 7], X[7, 15, 8, 14], X[15, 2, 16, 3], X[5, 12, 6, 13],		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 6, 2, 7], X[7, 15, 8, 14], X[15, 2, 16, 3], X[5, 12, 6, 13],
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 122]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_122_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 122]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_122_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 122]]&) /@ {~~SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>~~		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki> (#[Knot[10, 122]]&) /@ {
			SymmetryType, UnknottingNumber, ThreeGenus,
			BridgeIndex, SuperBridgeIndex, NakanishiIndex
			}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 3, 3, NotAvailable, 2}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 3, 3, NotAvailable, 2}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 122]][t]</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 122]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:33, 30 August 2005

2005-08-30T14:33:58Z

Show changes

DrorsRobot at 01:00, 30 August 2005

2005-08-30T01:00:53Z

← Older revision		Revision as of 21:00, 29 August 2005
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	</table>		</table>

			{\| width=100%
	See/edit the [[Rolfsen_Splice_Template]].		\|align=left\|See/edit the [[Rolfsen_Splice_Template]].

			Back to the [[#top\|top]].
			\|align=right\|{{Knot Navigation Links\|ext=gif}}
			\|}

	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:00, 29 August 2005

2005-08-29T22:00:00Z

Show changes

ScottTestRobot at 00:06, 29 August 2005

2005-08-29T00:06:28Z

← Older revision		Revision as of 20:06, 28 August 2005
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	<span id="top"></span>		<span id="top"></span>
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	<!-- this relies on transclusion for next and previous links -->		<!-- this relies on transclusion for next and previous links -->
	{{Knot Navigation Links\|ext=gif}}		{{Knot Navigation Links\|ext=gif}}

		⚫	{{Rolfsen Knot Page Header\|n=10\|k=122\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,-6,7,-4,1,-2,8,-5,6,-9,4,-10,2,-3,9,-7,5,-8,10/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=122\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,3,-6,7,-4,1,-2,8,-5,6,-9,4,-10,2,-3,9,-7,5,-8,10/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
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	<td width=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>		<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>
	<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>-9</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

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	q t + 4 q t + q t</nowiki></pre></td></tr>		q t + 4 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:45, 28 August 2005

2005-08-28T01:45:00Z

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ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:08Z

Resetting knot page to basic template.

New page

10 122 - Revision history

ScottTestRobot at 21:58, 1 September 2005

DrorsRobot at 22:41, 31 August 2005

ScottKnotPageRobot at 14:33, 30 August 2005

DrorsRobot at 01:00, 30 August 2005

DrorsRobot at 22:00, 29 August 2005

ScottTestRobot at 00:06, 29 August 2005

ScottTestRobot at 01:45, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.